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Welcome to our Math lesson on Expanding Brackets Summary, this is the seventh lesson of our suite of math lessons covering the topic of Expanding Brackets, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
Summarizing Everything Discussed So Far
Now, it is the time to solve a long exercise that summarizes everything discussed so far in this tutorial.
Example 7
Expand and simplify the following algebraic expression
4x ∙ (x - 1)(x - 2)(2x + 1) - (6x - 10) ÷ 2
Solution 7
Using the properties of expanding brackets yields
4x ∙ (x - 1)(x - 2)(2x + 1) - (6x - 10) ÷ 2
= 4x ∙ [x ∙ (x - 2)(2x + 1) - 1 ∙ (x - 2)(2x + 1)] - (6x - 10) ÷ 2
= 4x2 ∙ (x - 2)(2x + 1) - 4x ∙ (x - 2)(2x + 1) - (6x - 10) ÷ 2
= 4x2 ∙ [x ∙ 2x + x ∙ 1 + (-2) ∙ 2x + (-2) ∙ 1] - 4x ∙ [x ∙ 2x + x ∙ 1 + (-2) ∙ 2x + (-2) ∙ 1] - (6x - 10) ÷ 2
= 4x2 ∙ [2x2 + x - 4x - 2] - 4x ∙ [2x2 + x - 4x - 2] - (6x - 10) ÷ 2
= 4x2 ∙ [2x2 - 3x - 2] - 4x ∙ [2x2 - 3x - 2] - (6x - 10) ÷ 2
= 4x2 ∙ 2x2 + 4x2 ∙ (-3x) + 4x2 ∙ (-2) - 4x ∙ 2x2 - 4x ∙ (-3x) - 4x ∙ (-2) - 6x ÷ 2 - (-10) ÷ 2
= 8x4 - 12x3 - 8x2 - 8x3 + 12x2 + 8x - 3x + 5
= 8x4 - 20x3 + 4x2 + 5x + 5
More Expanding Brackets Lessons and Learning Resources
Expressions Learning Material| Tutorial ID | Math Tutorial Title | Tutorial | Video
Tutorial | Revision
Notes | Revision
Questions |
|---|
| 6.2 | Expanding Brackets | | | | |
| Lesson ID | Math Lesson Title | Lesson | Video
Lesson |
|---|
| 6.2.1 | How to remove the brackets from an Algebraic Expression when no Operations are involved | | |
| 6.2.2 | How to expand brackets when a number multiplies the Expression inside them | | |
| 6.2.3 | How to expand brackets when the Expression inside them Divides a Number | | |
| 6.2.4 | How to expand brackets when a Number Divides an Expression inside them | | |
| 6.2.5 | How to expand two Expressions inside Brackets Multiplied together | | |
| 6.2.6 | How to expand three or more Expressions inside Brackets Multiplied together | | |
| 6.2.7 | Expanding Brackets Summary | | |
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- Continuing learning expressions - read our next math tutorial: Special Algebraic Identities Obtained through Expanding
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